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Artificial Agents Play the Beer Game Eliminate the Bullwhip Effect and Whip the MBAs. Steven O. Kimbrough D.-J. Wu Fang Zhong FMEC, Philadelphia, June 2000; file: beergameslides.ppt. The MIT Beer Game. Players Retailer, Wholesaler, Distributor and Manufacturer. Goal

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artificial agents play the beer game eliminate the bullwhip effect and whip the mbas

Artificial Agents Play the Beer Game Eliminate the Bullwhip Effect and Whip the MBAs

Steven O. Kimbrough

D.-J. Wu

Fang Zhong

FMEC, Philadelphia, June 2000; file: beergameslides.ppt

the mit beer game
The MIT Beer Game
  • Players
    • Retailer, Wholesaler, Distributor and Manufacturer.
  • Goal
    • Minimize system-wide (chain) long-run average cost.
  • Information sharing: Mail.
  • Demand: Deterministic.
  • Costs
    • Holding cost: $1.00/case/week.
    • Penalty cost: $2.00/case/week.
  • Leadtime: 2 weeks physical delay
timing
Timing

1. New shipments delivered.

2. Orders arrive.

3. Fill orders plus backlog.

4. Decide how much to order.

5. Calculate inventory costs.

the bullwhip effect
The Bullwhip Effect
  • Order variability is amplified upstream in the supply chain.
  • Industry examples (P&G, HP).
bullwhip effect example p g
Bullwhip Effect Example (P & G)

Lee et al., 1997, Sloan Management Review

analytic results deterministic demand
Analytic Results: Deterministic Demand
  • Assumptions:
    • Fixed lead time.
    • Players work as a team.
    • Manufacturer has unlimited capacity.
  • “1-1” policy is optimal -- order whatever amount is ordered from your customer.
analytic results stochastic demand chen 1999 management science
Analytic Results: Stochastic Demand (Chen, 1999, Management Science)
  • Additional assumptions:
    • Only the Retailer incurs penalty cost.
    • Demand distribution is common knowledge.
    • Fixed information lead time.
    • Decreasing holding costs upstream in the chain.
  • Order-up-to (base stock installation) policy is optimal.
agent based approach
Agent-Based Approach
  • Agents work as a team.
  • No agent has knowledge on demand distribution.
  • No information sharing among agents.
  • Agents learn via genetic algorithms.
  • Fixed or stochastic leadtime.
research questions
Research Questions
  • Can the agents track the demand?
  • Can the agents eliminate the Bullwhip effect?
  • Can the agents discover the optimal policies if they exist?
  • Can the agents discover reasonably good policies under complex scenarios where analytical solutions are not available?
agents coding strategy
Agents Coding Strategy
  • Bit-string representation with fixed length n.
  • Leftmost bit represents the sign of “+” or “-”.
  • The rest bits represent how much to order.
  • Rule “x+1” means “if demand is x then order x+1”.
  • Rule search space is 2n-1 – 1.
experiment 1a first cup
Experiment 1a: First Cup
  • Environment:
    • Deterministic demand with fixed leadtime.
    • Fix the policy of Wholesaler, Distributor and Manufacturer to be “1-1”.
    • Only the Retailer agent learns.
  • Result: Retailer Agent finds “1-1”.
experiment 1b
Experiment 1b
  • All four Agents learn under the environment of experiment 1a.
  • Über rule for the team.
  • All four agents find “1-1”.
result of experiment 1b
Result of Experiment 1b

All four agents can find the optimal “1-1” policy

stability experiment 1b
Stability (Experiment 1b)
  • Fix any three agents to be “1-1”, and allow the fourth agent to learn.
  • The fourth agent minimizes its own long-run average cost rather than the team cost.
  • No agent has any incentive to deviate once the others are playing “1-1”.
  • Therefore “1-1” is apparently Nash.
experiment 2 second cup
Experiment 2: Second Cup
  • Environment:
    • Demand uniformly distributed between [0,15].
    • Fixed lead time.
    • All four Agents make their own decisions as in experiment 1b.
  • Agents eliminate the Bullwhip effect.
  • Agents find better policies than“1-1”.
slide21
Artificial agents discover a better policy than “1-1” when facing stochastic demand with penalty costs for all players.
experiment 3 third cup
Experiment 3: Third Cup
  • Environment:
    • Lead time uniformly distributed between [0,4].
    • The rest as in experiment 2.
  • Agents find better policies than “1-1”.
  • No Bullwhip effect.
  • The polices discovered by agents are Nash.
slide23
Artificial agents discover better and stable policies than “1-1” when facing stochastic demand and stochastic lead-time.
slide24
Artificial Agents are able to eliminate the Bullwhip effect when facing stochastic demand with stochastic leadtime.
the columbia beer game
The Columbia Beer Game
  • Environment:
    • Information lead time: (2, 2, 2, 0).
    • Physical lead time: (2, 2, 2, 3).
    • Initial conditions set as Chen (1999).
  • Agents find the optimal policy: order whatever is ordered with time shift, i.e.,

Q1 = D (t-1), Qi = Qi-1 (t – li-1).

ongoing research more beer
Ongoing Research: More Beer
  • Value of information sharing.
  • Coordination and cooperation.
  • Bargaining and negotiation.
  • Alternative learning mechanisms: Classifier systems.
summary
Summary
  • Agents are capable of playing the Beer Game
    • Track demand.
    • Eliminate the Bullwhip effect.
    • Discover the optimal policies if exist.
    • Discover good policies under complex scenarios where analytical solutions not available.
  • Intelligent and agile supply chain.
  • Multi-agent enterprise modeling.